Stochastic inequalities for \(M/G/1\) retrial queues with vacations and constant retrial policy. (English) Zbl 1185.90041

Summary: We consider an \(M/G/1\) retrial queue with vacations and we derive several stochastic comparison properties in the sense of strong stochastic ordering and convex ordering. The stochastic inequalities provide simple insensitive bounds for the stationary queue length distribution.


90B22 Queues and service in operations research


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[1] Falin, G. I.; Templeton, J. G.C., Retrial Queues (1997), Chapman and Hall: Chapman and Hall London · Zbl 0944.60005
[2] Falin, G. I., A survey of retrial queues, Queueing Systems, 7, 127-168 (1990) · Zbl 0709.60097
[3] Artalejo, J. R.; Falin, G., Standard and retrial queueing systems: A comparative analysis, Revista Mathematica Computense, 15, 101-129 (2002) · Zbl 1009.60079
[4] Levy, Y.; Yechiali, U., Utilization of idle time in an \(M / G / 1\) queueing system, Management Science, 22, 202-211 (1975) · Zbl 0313.60067
[5] Artalejo, J. R., Analysis of an \(M / G / 1\) queue with constant repeated attempts and server vacations, Computers and Operations Research, 24, 493-504 (1997) · Zbl 0882.90048
[6] Li, H.; Yang, T., A single-server retrial queue with server vacations and a finite number of input sources, Computers and Operations Research, 85, 149-160 (1995) · Zbl 0912.90139
[7] Zhang, Z. G.; Tian, N., Analysis of queueing systems with synchronous single vacation for some servers, Queueing Systems: Theory and Applications, 45, 161-175 (2003) · Zbl 1036.90033
[8] Langaris, C.; Moutzoukis, E., A retrial queue with structured batch arrivals, priorities and server vacations, Queueing Systems, 20, 341-368 (1995) · Zbl 0847.90059
[9] Krishna Kumar, B.; Arivudainambi, D., The \(M / G / 1\) retrial queue with Bernoulli schedules and general retrial times, Computers and Mathematics with Applications, 43, 15-30 (2002) · Zbl 1008.90010
[10] Stoyan, D., Comparison Methods for Queues and Other Stochastic Models (1983), Wiley: Wiley New York
[11] Müller, A.; Stoyan, D., Comparison Methods for Stochastic Models and Risk (2002), John Wiley and Sons, Ltd.
[12] Heidergott, B.; Vázquez-Abad, F., Measure valued differentiation for Markov chains, Journal of Optimization and Applications, 136, 187-209 (2008) · Zbl 1149.90173
[13] Heidergott, B.; Vázquez-Abad, F., Measure valued differentiation for random horizon problems, Markov Process and Related Fields, 12, 509-536 (2006) · Zbl 1117.60073
[14] Heidergott, B.; Hordijk, A.; Weißhaupt, H., Measure-valued differentiation for stationary Markov chains, Mathematics of Operations Research, 31, 154-172 (2006) · Zbl 1278.90428
[15] Cassandras, C. G.; Lafortune, S., Introduction to Discrete Event Systems (2007), Springer: Springer New York
[16] Liang, H. M.; Kulkarni, V. G., Monotonicity properties of single server retrial queues, Stochastic Models, 9, 373-400 (1993) · Zbl 0777.60091
[17] Khalil, Z.; Falin, G., Stochastic inequalities for M/G/1 retrial queues, Operations Research Letters, 16, 285-290 (1994) · Zbl 0819.60090
[18] Liang, H. M., Service station factors in monotonicity of retrial queues, Mathematical and Computer Modelling, 30, 189-196 (1999) · Zbl 1042.60544
[19] Choi, B. D.; Shin, Y. W.; Ahn, W. C., Retrial queues with collision arising from unslotted CSMA/CD protocol, Queueing Systems, 11, 335-356 (1992) · Zbl 0762.60088
[20] Neuts, M. F.; Ramalhoto, M. F., A service model in which the server is required to search for customers, Journal of Applied Probability, 21, 157-166 (1984) · Zbl 0531.60089
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